Nonlinear least squares analysis of catalytic rate models

Abstract

Conventional data generation and analysis procedures used to select a descriptive HougenWatson reaction rate model have been reviewed and some statistical objections to these conventional procedures have been presented. In an attempt to assess the practical importance of these objections, a recently published example was analyzed with both conventional techniques and nonlinear least squares procedures, which more closely conform to theoretical weighting requirements. Comparisons were made between the results of the conventional linear least squares analysis of isothermal data and those of nonlinear least squares analyses of both isothermal and nonisothermal data. It was found that the nonlinear least squares procedures were useful for a rational selection of an acceptable model and estimation of its parameters.General observations were made concerning good regions for further experimentation if a discrimination among rival models is desired. Additional well-designed experiments were found to be necessary to allow a reduction of the confidence region of the parameters of the HougenWatson models to an acceptable size.Often it is desired to fit rate data from a heterogeneous reaction to a model, either theoretical, semitheoretical, or empirical, to predict the reaction rate within the ranges of the variables studied and, in some cases, to allow cautious extrapolation. This perhaps most frequently has been done with a family of Hougen-Watson models (1, 2 ) as functional forms, from which one appropriate model hopefully could be selected by utilizing existing data. It is common to linearize these expressions by a rearrangement of the model so that the constants within them can be estimated by the method of unweighted linear least squares or some other simple technique. These models must then be screened to reject those that are inadequate in the light of the data.Many criteria have been proposed for the elimination of unsatisfactory models. For example, models have been declared inadequate if the estimated adsorption or rate constants were negative, if the temperature coefficients of these estimated parameter values were of the wrong sign, or if the ability of the models in question to reproduce the data with these parameter values were unacceptable. Occasionally one, but very frequently more than one, model can be said to be plausible after following a conventional procedure such as this.Several objections to the Hougen-Watson models have been published and it is not necessarily the authors' intent in this paper to endorse these models, even though numerous useful applications of such models exist. Apart from these theoretical inadequacies of the Hougen-Watson models, however, several objections have been raised concerning the statistical judiciousness of this conventional approach to the analysis of heterogeneous reaction rate data ( 3 to 5 ) . These statistical considerations suggest that the conventional methods are motivated more by the requirement of an expedient analysis than by statistical justification. An an...

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